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1.
Stephen J. Gardiner 《Proceedings of the American Mathematical Society》1998,126(9):2699-2703
Let be open and be a bounded set which is closed relative to . We characterize those pairs such that, for each harmonic function on which is uniformly continuous on , there is a sequence of harmonic polynomials which converges to uniformly on . As an immediate corollary we obtain a characterization of Mergelyan pairs for harmonic functions.
2.
Sufficient conditions for one domain to contain another in a space of constant curvature 总被引:4,自引:0,他引:4
Jiazu Zhou 《Proceedings of the American Mathematical Society》1998,126(9):2797-2803
As an application of the analogue of C-S. Chen's kinematic formula in the 3-dimensional space of constant curvature , that is, Euclidean space , -sphere , hyperbolic space (, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space , or a -sphere or a hyperbolic space .
3.
Let be a finite -solvable group for different primes and . Let and be such that . We prove that every of -degree has -degree if and only if and .
4.
Jutta Hausen Phillip Schultz 《Proceedings of the American Mathematical Society》1998,126(9):2525-2533
Let be a prime number and let be an abelian -group. Let be the maximal normal -subgroup of and the maximal -subgroup of its centre. Let be the torsion radical of . Then . The result is new for and 3, and the proof is new and valid for all primes .
5.
Tin-Yau Tam 《Proceedings of the American Mathematical Society》1998,126(9):2607-2614
Let be an Hermitian matrix with where are the ordered eigenvalues of . A result of Ky Fan (1949) asserts that if and are Hermitian matrices, then is majorized by . We extend the result in the framework of real semisimple Lie algebras in the following way. Let be a noncompact real semisimple Lie algebra with Cartan decomposition . We show that for any given , , where is the unique element corresponding to , in a fixed closed positive Weyl chamber of a maximal abelian subalgebra of in . Here the ordering is induced by the dual cone of . Fan's result corresponds to the Lie algebra . The compact case is also discussed. As applications, two unexpected singular values inequalities concerning the sum of two real matrices and the sum of two real skew symmetric matrices are obtained.
6.
Abdelbaki Boutabaa Alain Escassut 《Proceedings of the American Mathematical Society》1998,126(9):2557-2568
Let be a complete ultrametric algebraically closed field of characteristic zero, and let be the field of meromorphic functions in . For all set in and for all we denote by the subset of : zero of order After studying unique range sets for entire functions in in a previous article, here we consider a similar problem for meromorphic functions by showing, in particular, that, for every , there exist sets of elements in such that, if have the same poles (counting multiplicities), and satisfy , then . We show how to construct such sets.
7.
S. Hassi H. S. V. de Snoo A. D. I. Willemsma 《Proceedings of the American Mathematical Society》1998,126(9):2663-2675
Let be a selfadjoint operator in a Hilbert space with inner product . The rank one perturbations of have the form , , for some element . In this paper we consider smooth perturbations, i.e. we consider for some . Function-theoretic properties of their so-called -functions and operator-theoretic consequences will be studied.
8.
Eve Oja 《Proceedings of the American Mathematical Society》1998,126(9):2747-2753
We prove that the space of compact operators on a Banach space is an -ideal in the space of bounded operators if and only if has the metric compact approximation property (MCAP), and is an -ideal in for all separable subspaces of having the MCAP. It follows that the Kalton-Werner theorem characterizing -ideals of compact operators on separable Banach spaces is also valid for non-separable spaces: for a Banach space is an -ideal in if and only if has the MCAP, contains no subspace isomorphic to and has property It also follows that is an -ideal in for all Banach spaces if and only if has the MCAP, and is an -ideal in .
9.
Michel Brion 《Proceedings of the American Mathematical Society》1998,126(9):2535-2539
Let be a smooth affine algebraic variety where a reductive algebraic group acts with a smooth quotient space . We show that the algebraic differential forms on which are pull-backs of forms on are exactly the -invariant horizontal differential forms on .
10.
Global iteration schemes for strongly pseudo-contractive maps 总被引:7,自引:0,他引:7
C. E. Chidume 《Proceedings of the American Mathematical Society》1998,126(9):2641-2649
Suppose is a real uniformly smooth Banach space, is a nonempty closed convex and bounded subset of , and is a strong pseudo-contraction. It is proved that if has a fixed point in then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in , converge strongly to the unique fixed . No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.
11.
Let be factors generated by a periodic tower of finite dimensional -algebras. We prove that for sufficiently large , is -isomorphic to a subalgebra of .
12.
Tianxuan Miao 《Proceedings of the American Mathematical Society》1998,126(12):3571-3579
Let be a -compact locally compact nondiscrete group and let be a -invariant ideal of . We denote the set of left invariant means on that are zero on (i.e. for all ) by . We show that, when is amenable as a discrete group and the closed -invariant subset of the spectrum of corresponding to is a -set, is very large in the sense that every nonempty -subset of contains a norm discrete copy of , where is the Stone- compactification of the set of positive integers with the discrete topology. In particular, we prove that has no exposed points in this case and every nonempty -subset of the set of left invariant means on contains a norm discrete copy of .
13.
Phan H. Loi 《Proceedings of the American Mathematical Society》1998,126(9):2651-2662
Given an irreducible inclusion of factors with finite index , where is of type , of type , , and are relatively prime positive integers, we will prove that if satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with . Relations between and a certain -kernel on subfactors are also discussed.
14.
R. Daniel Mauldin Ká roly Simon 《Proceedings of the American Mathematical Society》1998,126(9):2733-2736
Since the 1930's many authors have studied the distribution of the random series where the signs are chosen independently with probability and . Solomyak recently proved that for almost every the distribution is absolutely continuous with respect to Lebesgue measure. In this paper we prove that is even equivalent to Lebesgue measure for almost all .
15.
R. N. Cruz K. A. de Rezende 《Proceedings of the American Mathematical Society》1998,126(12):3715-3720
We show that the cycle-rank of a Lyapunov graph on a manifold satisfies: , where is the genus of . This generalizes a theorem of Franks. We also show that given any integer with , for some Lyapunov graph on .
16.
Let be a finite irreducible complex linear group with -power degree, where is a prime number. Then every -subgroup of that is normalized by a Sylow -subgroup must be abelian. This and related results are proved using an elementary character-theoretic argument.
17.
M. I. Berenguer A. R. Villena 《Proceedings of the American Mathematical Society》1998,126(9):2717-2720
Let and be centrally closed prime complex Banach algebras with linear involution. If is semisimple, then any Lie derivation of the skew elements of is continuous and any Lie isomorphism from the skew elements of onto the skew elements of is continuous.
18.
Eberhard Kaniuth Gitta Kutyniok 《Proceedings of the American Mathematical Society》1998,126(12):3561-3569
Let be a locally compact abelian group. The notion of Zak transform on extends to . Suppose that is compactly generated and its connected component of the identity is non-compact. Generalizing a classical result for , we then prove that if is such that its Zak transform is continuous on , then has a zero.
19.
Toshihiro Okuyama Keiichi Watanabe 《Proceedings of the American Mathematical Society》1998,126(9):2631-2634
Let and be bounded linear operators, and let be a partial isometry on a Hilbert space. Suppose that (1) , (2) , (3) and (4) . Then we have .
20.
Torben Maack Bisgaard 《Proceedings of the American Mathematical Society》1998,126(11):3227-3237
For a certain constant (a little less than ), every function satisfying , , is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence there is a positive definite matrix sequence which is not of positive type and which satisfies , . For a certain constant (a little greater than ), for every function satisfying , , there is a convolution semigroup of measures on , with moments of all orders, such that , , and for every such convolution semigroup the measure is Stieltjes indeterminate for all .